Hmm, VERY interesting! Thanks for opening the discussion, and I look forward to reading what others may have to add.

The fact that we now use Poly or Fiber wads in our target loads not only protect the base from the powder impacting the base but could they also stop the angular deformation that Mann found?  Wads normally increased the accuracy of the bullet in my experience.  Never recovered bullets just saw results on target at 600 yards.

This is indeed a very interesting topic.  Plus being a bear of smallish brain, it gave rise to this thought.  The point here seems to be that one accuracy help is not disturbing the uniformity of the base and its squareness with the vertical axis of the bullet.  Therefore, were it possible to cast such, would a bullet with a perfectly domed base not only be as accurate as a square base but also less likely to acquire an oblique base?

Also, is it always or at least almost always 1-in 5?  If so, why?

Bill Lawrence

The biggest thing concerning me with a oblique base is how it's affected as it leaves the muzzle. It would be no different than a flat base on a oblique crown, and will kick the bullet's base to one side as it exits. This instability induced upon exiting the bore would have huge affects on accuracy, and destabilize the bullet instantly as it exits the barrel.

No doubt the bullets shown would have trouble shooting a clover leaf at any distance, but the big question is how they got the shape they are showing.

My first thought is poor casting. The right hand bullet with the most deformation, shows no sign of compression in the bottom lube groove. Maybe with careful measurement it would. That would seem to indicate a soft spot or void in the base.

Mann also had photos of bullets he had cast where the tips were cut off and wire inserted into the voids found. Those examples would correspond to the angles of the bases shown. I don't remember a mention of doing the same at the base.

A proper test would be near impossible. Choose a perfect bullet and measure. Load it, pull it and remeasure. Load it again and shoot it. Only then would you know when the deformity happened and under the which pressure.

I suspect that this is one of the reasons that Pope was a proponent of muzzle loading. The direction of engraving the bullets would have much less effect on flight consistency than the deformation to the base of the bullets shown, if it happened during loading. Compressing an uneven powder column with a bullet or a poor start breech seating seems to make more sense than uneven gas pressure in a cylinder.

Link to page 262 showing wires in the bullets with voids and part of this discussion

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Dellet
That last image of the three bullets with square and oblique bases is purely to show the angle of the oblique bases as discussed by Mann. Those are Photo Shopped images that I distorted for illustrative purposes and not actual recovered bullets. Perhaps I should have been more specific about that point.
Bill
The 1-in-5 according to Mann's findings was an average. 1-in-5 was random as was the amount bullet-to-bullet base deformation.
cheatin_charlie
Some of Mann's tests were fired with no wad, others with Leopold's Oleo wads. Bullet base deformation randomly occurred with or without wads.
gunlaker
Thank you for that image with Pope's notes. I downloaded and will read later.

If the deformity is random, then so is the cause. 

Assuming the rest of the loading process was tightly controlled and looking at the quality of the bullets shown in the link provided, I still lean in that direction.

Something else to consider was in a new book I was just reading. It seems there was a corresponding jump in competition scores with the adoption of semi-smokeless powders. 
Could base deformation, or lack of, be part of that reason?